select the correct answer. what is $sqrt{192}$ in simplest form?\na. $32sqrt{3}$\nb. $3sqrt{8}$\nc…
select the correct answer. what is $sqrt{192}$ in simplest form?\na. $32sqrt{3}$\nb. $3sqrt{8}$\nc. $8sqrt{3}$\nd. $2sqrt{48}$
Answer
Answer:
C. $8\sqrt{3}$
Explanation:
Step1: Prime - factorize 192
$192 = 2\times96=2\times2\times48 = 2\times2\times2\times24=2\times2\times2\times2\times12=2\times2\times2\times2\times2\times6=2^6\times3$
Step2: Apply square - root property
$\sqrt{192}=\sqrt{2^6\times3}$ Since $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ ($a = 2^6$, $b = 3$), we have $\sqrt{192}=\sqrt{2^6}\times\sqrt{3}$
Step3: Simplify $\sqrt{2^6}$
$\sqrt{2^6}=2^3 = 8$ So, $\sqrt{192}=8\sqrt{3}$